In short, the Kiowa tribe become great hunters due to the help of the Sun god and their close relationship with three animals:  the horse, the dog, and the buffalo. 

In order to understand the relationship of the three animals to Kiowa hunting, one must understand the importance of the horse and the dog and the buffalo to the Kiowa creation myth and Kiowa history.  First, the tribe is only able to emerge after the domesticated horse appears on the Northern Plains.  Horses are the Kiowa tribe's main method of transportation and the reason the Kiowa are able to migrate.  In this way, the horse is what allows the Kiowa freedom to explore the Great Plains. 

Two other animals important to the Kiowa tribe in regards to hunting are dogs and buffalo.  Dogs are always important to the Kiowa tribe.  In fact, the Kiowa obtain their first domesticated dog when one speaks to a hunter and saves him from enemy warriors.  Lastly, because buffalo are the Kiowa's main source of sustenance, this animal has always been important to them being good hunters.  Even in their myth system, there is a hunter who escapes from a magic buffalo. 

In conclusion, it is important not to neglect the importance of the Sun god in regards to the hunting prowess of the Kiowa.  Kiowa hunters could only be certain of a successful hunt if they danced the Sun Dance and proved their worth in that way.  Further, the decline of the Kiowa tribe is certainly related to the massacre of the horses and the buffalo in the latter half of the nineteenth century.